Chapter 8.CT, Problem 16CT

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

The area of a right triangle whose sides have lengths5 in., 12 in,. and 13 in. is exactly 30 in2. Use the formula A = 1 2 r P to find the length of the radius of the circle thatcan be inscribed in this tringle.

To determine

To find:

The length of the radius of the circle that can be inscribed in the tringle.

Explanation

Given:

The area of a right triangle whose sides have lengths 5 in, 12 in, and 13 in is exactly 30 in2.

Theorem:

The area A of a triangle whose perimeter is P and has the length of the radius r of its inscribed circle is given by A=12rP.

From the given, let a=5 in, b=12 in, c=13 in, and A=30 in2.

The perimeter is, P=a+b+c=5+12+13=30 in

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